Abstract : This thesis is devoted to the study of scattering theory for Dirac fields in various spacetimes of General Relativity. Thetime-dependent methods developed by Enss, Sigal, Soffer, Graf,Derezi\'nski and Gérard are the backbone of thiswork. These methods are based on propagation estimates, such as minimalvelocity estimates (obtained using a Mourre theory) that are a weakform of the Huygens principle, and on the study of natural and intuitive asymptotic observables such as theasymptotic velocity operators. They turn out to be extremelyconvenient when studying relativistic equations since they areintimately related to the fundamental structure of GeneralRelativity: the light cone. We first test these methods studying theasymptotic behaviour of Dirac fields perturbed by long-range potentialsin flat spacetime and we prove the existence and asymptoticcompleteness of modified wave operators. We then consider morecomplicated geometrical situations: the propagation of Diracfields in the exterior region of a Reissner-Nordström black hole(spherically symmetric) and a Kerr-Newman black hole (in rotation) fromthe point of view of observers static at infinity. The peculiarity ofsuch situations is that the observer perceives two asymptotic regions(the horizon of the black hole and spacelike infinity) having verydifferent geometrical structures; this leads to the existence of twodistinct scattering channels. In the case of spherically symmetricblack holes, we can use a decomposition into spherical harmonics inorder to obtain a Dirac equation with potentials on one dimensionalflat spacetime. The main difficulty in the Kerr-Newman case comes fromthe absence of spherical symmetry. In both cases, we prove theexistence and asymptotic completeness of (modified at infinity) wave operators by means of theprevious time-dependent methods.